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In this work we address reliable file delivery over mobile broadcast networks, concentrating on the Raptor codes as specified for Multimedia Broadcast/Multicast Services (MBMS) within 3GPP. We start by describing Luby-Transform (LT) codes, which are the first practical fountain codes. Then, using a natural and easy to understand linear algebra notation, we describe Raptor codes as a powerful extension of LT codes. We provide some insight into the Raptor code structure and some guidelines for implementation of encoders and decoders. Finally, some selected simulations verify the good performance of file distribution with Raptor codes as specified in 3GPP. References to a complete set of simulation results are also provided.

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We have measured the critical velocity vc at which 3 He-A in a rotating cylinder becomes unstable against the formation of quantized vortex lines with continuous (singularity-free) core structure. We find that vc is distributed between a maximum and minimum limit, which we ascribe to a dependence on the texture of the orbital angular momentuml(r) in the cylinder. Slow cool down through Tc in rotation yieldsl(r) textures for which the measured vc's are in good agreement with the calculated instability of the expectedl texture.PACS numbers: 67.57. Fg, 05.70Fh A first order transition from one phase to another is associated with hysteresis because of the difficulty of nucleating the new phase. Two effects generally reduce the hysteresis. Firstly, thermal or quantum fluctuations cause the new phase to appear before the energy barrier separating the two energy minima vanishes. Secondly, surfaces, impurities, or other external agents reduce the energy barrier from its intrinsic value. Both phenomena are of crucial importance for the long standing problem of critical velocities and vortex nucleation in superfluids [1], but occur also in more usual phenomena like formation of water droplets or gas bubbles [2]. The purpose of the present work is to study an exceptional case of vortex nucleation where neither fluctuations nor external surfaces should play a role: superfluid 3 He-A.In usual superfluids and superconductors the phase slip takes place by creation and motion of zeros in the order parameter [3]. The A phase of 3 He is exceptional because the phase slip arises from the motion of the local angular momentum axisl(r). The characteristic length scale of thel(r) texture is macroscopic ∼ 10 µm. Therefore all thermal and quantum fluctuations are negligible. Moreover, a rigid boundary condition fixesl perpendicular to the wall of the experimental container. Thus the processes responsible for the critical velocity take place further than 10 µm from the wall, beyond the reach of surface roughness. Instead, the critical velocity v c for the phase slip depends on the initiall texture. We measure the critical velocity in a rotating cylinder, and find that it may vary within a factor of 6. However, by cooling slowly through the superfluid transition temperature T c in rotation, the equilibrium texture is created and the measured v c is in agreement with theoretical calculations.Anisotropic superflow.-In ordinary superconductors and superfluids, the order parameter has a phase factor exp[iφ(r)], and the superfluid velocity is defined as the gradient of the phase, v s ∝ ∇φ. In 3 He-A there is an additional phase factor exp[iφ l (p)], which depends on the azimuthal angle φ l of the quasiparticle momentum p with respect to the angular momentum axisl. Instead of resolving the two phases separately, one may only define the total phase factor, which can be expressed as (m + in) ·p. Herel,m, andn form an orthonormal triad, which generally depends on the location r. The superfluid velocity is defined as v s =h 2m km k ∇n k , where ...